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2 years ago

If the length of a rectangle is halved and its breath is tripled, what is the percentage change in its area??

Mathematics

1 answer:

Dennis_Churaev [7]2 years ago

6 0

Answer:

A 50% increase

Step-by-step explanation:

Area = length x breadth

Let illustrate this with an example

original dimensions

length = 4

breadth = 5

area = 4 x 5 = 20

new dimensions

length = 4/2 = 2

breadth = 5 x 3 = 15

area = 15 x 2 = 30

Percentage change = 30 - 20 / 20 x 100 = 50%

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Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots StartRoo

anastassius [24]

Answer:

$a) f(x)=3x^{3}-6x^{2}-15x+30$

Step-by-step explanation:

1) In this question we've been given "a", the leading coefficient. and two roots:

$x_{1}=\sqrt{5}\:x_{2}=2$

2) There's a theorem, called the Irrational Theorem Root that states:

If one root is in this form $x'=\sqrt{a}+b$ then its conjugate $x''=\sqrt{a}-b$ . is also a root of this polynomial.

Therefore

$x_3=-\sqrt{5}$

3) So, applying this Theorem we can rewrite the equation, by factoring. Remembering that x is the root. Since the question wants it in this expanded form then:

$f(x)=3(x-\sqrt{5})(x+\sqrt{5})(x-2)\Rightarrow 3x^{3}-6x^{2}-15x+30$